Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling

Myoung-jae Lee, Sanghyeok Lee

Research output: Chapter in Book/Report/Conference proceedingChapter

1 Citation (Scopus)

Abstract

Standard stratified sampling (SSS) is a popular non-random sampling scheme. Maximum likelihood estimator (MLE) is inconsistent if some sampled strata depend on the response variable Y ('endogenous samples') or if some Y-dependent strata are not sampled at all ('truncated sample' - A missing data problem). Various versions of MLE have appeared in the literature, and this paper reviews practical likelihood-based estimators for endogenous or truncated samples in SSS. Also a new estimator 'Estimated- EX MLE' is introduced using an extra random sample on X (not on Y) to estimate the distribution EX of X. As information on Y may be hard to get, this estimator's data demand is weaker than an extra random sample on Y in some other estimators. The estimator can greatly improve the efficiency of 'Fixed-X MLE' which conditions on X, even if the extra sample size is small. In fact, Estimated-EXMLE does not estimate the full FX as it needs only a sample average using the extra sample. Estimated-EX MLE can be almost as efficient as the 'Known-F XMLE'. A small-scale simulation study is provided to illustrate these points.

Original languageEnglish
Title of host publicationAdvances in Econometrics
Pages63-91
Number of pages29
Volume27 A
DOIs
Publication statusPublished - 2011 Dec 1

Publication series

NameAdvances in Econometrics
Volume27 A
ISSN (Print)07319053

Fingerprint

Estimator
Stratified sampling
Maximum likelihood estimator
Missing data
Sample size
Sampling
Simulation study

Keywords

  • Choicebased sampling
  • Endogenous sampling
  • Standard stratified sampling
  • Truncated regression

ASJC Scopus subject areas

  • Economics and Econometrics

Cite this

Lee, M., & Lee, S. (2011). Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling. In Advances in Econometrics (Vol. 27 A, pp. 63-91). [17004564] (Advances in Econometrics; Vol. 27 A). https://doi.org/10.1108/S0731-9053(2011)000027A006

Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling. / Lee, Myoung-jae; Lee, Sanghyeok.

Advances in Econometrics. Vol. 27 A 2011. p. 63-91 17004564 (Advances in Econometrics; Vol. 27 A).

Research output: Chapter in Book/Report/Conference proceedingChapter

Lee, M & Lee, S 2011, Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling. in Advances in Econometrics. vol. 27 A, 17004564, Advances in Econometrics, vol. 27 A, pp. 63-91. https://doi.org/10.1108/S0731-9053(2011)000027A006
Lee M, Lee S. Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling. In Advances in Econometrics. Vol. 27 A. 2011. p. 63-91. 17004564. (Advances in Econometrics). https://doi.org/10.1108/S0731-9053(2011)000027A006
Lee, Myoung-jae ; Lee, Sanghyeok. / Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling. Advances in Econometrics. Vol. 27 A 2011. pp. 63-91 (Advances in Econometrics).
@inbook{bd510d17586f4c0db4d96f9f251de7c1,
title = "Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling",
abstract = "Standard stratified sampling (SSS) is a popular non-random sampling scheme. Maximum likelihood estimator (MLE) is inconsistent if some sampled strata depend on the response variable Y ('endogenous samples') or if some Y-dependent strata are not sampled at all ('truncated sample' - A missing data problem). Various versions of MLE have appeared in the literature, and this paper reviews practical likelihood-based estimators for endogenous or truncated samples in SSS. Also a new estimator 'Estimated- EX MLE' is introduced using an extra random sample on X (not on Y) to estimate the distribution EX of X. As information on Y may be hard to get, this estimator's data demand is weaker than an extra random sample on Y in some other estimators. The estimator can greatly improve the efficiency of 'Fixed-X MLE' which conditions on X, even if the extra sample size is small. In fact, Estimated-EXMLE does not estimate the full FX as it needs only a sample average using the extra sample. Estimated-EX MLE can be almost as efficient as the 'Known-F XMLE'. A small-scale simulation study is provided to illustrate these points.",
keywords = "Choicebased sampling, Endogenous sampling, Standard stratified sampling, Truncated regression",
author = "Myoung-jae Lee and Sanghyeok Lee",
year = "2011",
month = "12",
day = "1",
doi = "10.1108/S0731-9053(2011)000027A006",
language = "English",
isbn = "9781780525242",
volume = "27 A",
series = "Advances in Econometrics",
pages = "63--91",
booktitle = "Advances in Econometrics",

}

TY - CHAP

T1 - Likelihood-based estimators for endogenous or truncated samples in standard stratified sampling

AU - Lee, Myoung-jae

AU - Lee, Sanghyeok

PY - 2011/12/1

Y1 - 2011/12/1

N2 - Standard stratified sampling (SSS) is a popular non-random sampling scheme. Maximum likelihood estimator (MLE) is inconsistent if some sampled strata depend on the response variable Y ('endogenous samples') or if some Y-dependent strata are not sampled at all ('truncated sample' - A missing data problem). Various versions of MLE have appeared in the literature, and this paper reviews practical likelihood-based estimators for endogenous or truncated samples in SSS. Also a new estimator 'Estimated- EX MLE' is introduced using an extra random sample on X (not on Y) to estimate the distribution EX of X. As information on Y may be hard to get, this estimator's data demand is weaker than an extra random sample on Y in some other estimators. The estimator can greatly improve the efficiency of 'Fixed-X MLE' which conditions on X, even if the extra sample size is small. In fact, Estimated-EXMLE does not estimate the full FX as it needs only a sample average using the extra sample. Estimated-EX MLE can be almost as efficient as the 'Known-F XMLE'. A small-scale simulation study is provided to illustrate these points.

AB - Standard stratified sampling (SSS) is a popular non-random sampling scheme. Maximum likelihood estimator (MLE) is inconsistent if some sampled strata depend on the response variable Y ('endogenous samples') or if some Y-dependent strata are not sampled at all ('truncated sample' - A missing data problem). Various versions of MLE have appeared in the literature, and this paper reviews practical likelihood-based estimators for endogenous or truncated samples in SSS. Also a new estimator 'Estimated- EX MLE' is introduced using an extra random sample on X (not on Y) to estimate the distribution EX of X. As information on Y may be hard to get, this estimator's data demand is weaker than an extra random sample on Y in some other estimators. The estimator can greatly improve the efficiency of 'Fixed-X MLE' which conditions on X, even if the extra sample size is small. In fact, Estimated-EXMLE does not estimate the full FX as it needs only a sample average using the extra sample. Estimated-EX MLE can be almost as efficient as the 'Known-F XMLE'. A small-scale simulation study is provided to illustrate these points.

KW - Choicebased sampling

KW - Endogenous sampling

KW - Standard stratified sampling

KW - Truncated regression

UR - http://www.scopus.com/inward/record.url?scp=84869156377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869156377&partnerID=8YFLogxK

U2 - 10.1108/S0731-9053(2011)000027A006

DO - 10.1108/S0731-9053(2011)000027A006

M3 - Chapter

AN - SCOPUS:84869156377

SN - 9781780525242

VL - 27 A

T3 - Advances in Econometrics

SP - 63

EP - 91

BT - Advances in Econometrics

ER -